Any real examples of formal logic necessary for solving scientific problems?

Discussion in 'Physics & Math' started by Speakpigeon, May 8, 2018.

  1. Michael 345 Bali in Nov closer Valued Senior Member

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    Sounds like a serious contender to me.

    Great work

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  3. Speakpigeon Registered Senior Member

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    I certainly don't know that our sense of logic is necessarily useful, or even just necessary at all for that matter. Yet, I don't see how we could possibly reason at all without it and I suspect it's very useful even outside reasoning proper, i.e. if we take reasoning to be conscious rational thinking. I suspect, and I would be very surprised to be wrong on that, that our brain does some basic logic pretty much all the time, including for a good chunk, if not all, of it's unconscious processes. That is, it does it even without telling us, so to speak. Still, I certainly wouldn't have any conclusive proof of that. All I can say is that I have logical intuitions, which I take to be logical evaluations delivered to my conscious mind by some unconscious brain processes working in the background. I guess it's up to each of us to make up their own mind as to what happens exactly when they have such logical intuitions.

    I think you are confusing logic with conceptual framework. If the conceptual framework is wrong, no amount of logic will make it right. You need first to change the conceptual framework and then use logic. What logic does, however, in this case, is that it will show you that whatever you can deduce from your current logical framework is inconsistent with observed facts. So, logic does tell you your framework is probably wrong. What it doesn't do, is tell you what new framework to put in its place. To do that, it seems you need a bit more than just logic, let's say, imagination. Still, some logic is necessary because it will tell you whether your new framework is consistent with facts.

    Now, the real question is whether our sense of logic is enough logic to do all that, or whether we need formal logic because, somehow, it's all too complicated or too complex.

    I'm not interested in "too complicated". I'm interested in "too complex". So, prove to me that what Schrödinger, Bohr, Einstein, Heisenberg and a few other bright fellows did was somehow so complex that they could only do it because formal logic was already at the time somehow at the core of modern science. I think I would be very sceptical about that. Still, I'm not a specialist of anything so that's why I'm asking.
    EB
     
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  5. Speakpigeon Registered Senior Member

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    No, I don't think so.

    I think what they did is pretty intuitive. It would seem obvious that we should expect that all our logical intuitions should have a formal expression, so merely couching an intuition into a formal expression isn't terribly convincing. And in this particular case, the formal expression you exhibit in your post shows that the logic of it is not even complex. Sure, 2 to the power of 24 is a lot, but I think our brain knows how to do without it.

    You have to keep in mind that specialists basically are people who train their brain to build abstract representations of their subject-matter. Once your brain can handle a bit of the real world through such abstractions, it can apply our sense of logic to them and it can work. At least that's how I see it.

    Still, thanks for a very concrete example. That's real science and a very explicit logical formula. Just not one terribly complex, you will admit, and therefore not too convincing.
    EB
     
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  7. Speakpigeon Registered Senior Member

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    Sorry, I missed the relevance of that!

    So, yes, it's logic, and it's applied, and it's necessary.

    But it's not complex at all. You could say it's very, very basic. And therefore intuitive. So formal logic is probably not necessary.

    The only difficulty would be the complication coming from the number of premises, which can obviously be very large in practical applications. So, I would say formal logic in this case is very convenient. You just use pen and paper to write down all the data and make sure you don't forget any, like you would for a long addition.

    Still, good point. Real science and actual logic. Just not complex enough to really necessitate the use of formal logic.
    EB
     
  8. arfa brane call me arf Valued Senior Member

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    I don't. I think a conceptual framework is necessarily a logical construction. What we "need" are good tools to help us visualise (however anyone manages this) those systems of interest we're . . . interested in.
    You should try to define, for everyone's benefit, what a "sense of logic" is, and also define "complex" and "complicated".
    You seem to have made some kind of mistaken conclusion.

    Schrodinger derived his equation via the "formal logic" of partial differential equations (and a few hints from Einstein, deBroglie and others). That his solution predicts electron orbitals (in Hydrogen, anyway) is entirely logical. Other predictions didn't seem to be very logical (entanglement for instance, which is still difficult to put in a "conceptual framework", for most people), but the equation was there. It still is there.

    What I was talking about was, at the time, Einstein, Schrodinger, Bohr etc saw just how illogical the new theory seemed to be, and concluded it must be somehow incomplete, or otherwise wrong. It isn't.

    Today, physics students around the world can derive Schrodinger's equation or at least understand how it follows from certain postulates (wave-particle duality, etc). It isn't a particularly complex problem. It would be a complicated problem though, if we didn't understand calculus and wave equations.
     
    Last edited: May 21, 2018
  9. iceaura Valued Senior Member

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    You have been handed at least four examples of the necessity of formal logic in modern scientific research: Use of computers, auditing and proof of argument validity, identification of assumptions and premises in failed investigation, and validation of relevant research questions or experiment design. (Bell's Theorem example, in my posting).
    The question is not one of complexity, but necessity: your underestimation of the difficulty of "simple" formal logical argument is an explanation, but not a reason, for your dismissal of the necessity of its employment.
    But it is necessary, in science.
    You have it backwards.
    It's the simple stuff that one handles via formal logic - breaking a complex problem into pieces or questions that can be handled via formal logic is a major advance in solving it.
    Formality of logic does not make complex reasoning easier. It makes it verifiable, reproducible, reliable, demonstrable, and effective.
    Formal logic is usually too difficult to use for more than suggestive guidance in primary investigation of new and complex situations - it is normally brought in afterwards, to audit and correct error and isolate assumptions and clean up the intuitions and verify experimental design and so forth. It allows people - the researcher as well as those the researcher communicates with - to follow and verify the argument being made.
    The intuition comes first, the difficult formalization of the argument comes second, in most cases.
     
    Last edited: May 21, 2018
  10. iceaura Valued Senior Member

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    Schrödinger, according to bio, guessed his equation. The derivation came afterwards.
     
  11. exchemist Valued Senior Member

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    Yes this seems to be typical in science. There is a creative leap to a hypothesis, which is then tested to see if it works. Not much formal logic in that process, usually.
     
  12. Michael 345 Bali in Nov closer Valued Senior Member

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    I think I was on the same wavelength but unable to express it as clearly

    Looking for formal logic to solve very complex problems seems to be a lost endeavour

    Breaking down the complexity to a level where formal logic can kick in seems to be "just" a insight on how the complex problem might be solved, but it insight has not been achieved via formal logic

    Complex problem
    Travel around the world using ONE transport vehicle

    Cannot
    Need various methods of transport

    Solved
    Build ONE transport vehicle which incorporates all the modes of travel

    Logical or not

    I don't know. Practical certainly not. Logical? Someone please judge

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  13. iceaura Valued Senior Member

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    The design of the "test" requires formal logical rigor, as does the interpretation of the results (often).
    I've been asking about the notation - whether "formal logic" as a term is in reality a reference to a particular notation and symbolism - but no answer yet.
     
  14. Beer w/Straw Transcendental Ignorance! Valued Senior Member

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    I kept thinking about cognitive psychology.

    As I can't see formal logic being used in romantic matters...
     
  15. Speakpigeon Registered Senior Member

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    Yes, a conceptual framework is a logical construction but it is also more than that. I agree you certainly need your different concepts to form a logically consistent system. But then you need to come up with the concepts to begin with and it's not logic that will give you that.

    Anyway, if you want to show Schrödinger needed formal logic you'll have to be a little more specific than that.

    I think I already provided the basic elements. I see evidence that we have a sense of logic in the fact that we seem able in some cases of valuating logical formulae without consciously going through any formal logical calculus. So the calculus must be done by some unconscious process, the result being delivered to our conscious mind. So, all we're conscious of will be the result, the logical value itself, true or false. I would assume there's a limit to the complexity of the formulae it can solve. And, obviously, that doesn't stop us to do it consciously and more formally, for example if we want to make sure. I would also assume that our sense of logic can only operate on predigested data. I suppose it can't deal directly with big amounts of data. So, as I see it, for complicated problems, you have to train you brain, so to speak, to build an abstract representation of the problem. To do that, you just work hard to become a specialist, an expert. Once the problem is abstracted, the logical relations between parts may become easy enough for your sense of logic to solve it on its own. Obviously, using formal logic is also one way to present a conveniently abstract representation of a problem to your sense of logic to solve it, but that doesn't seem necessary to me, only convenient. This would explain why it seems only the specialists of mathematical logic use it at all. Each scientist will be an expert in his own field and his brain will be trained to deal with the subject-matter and must have the required abstract representations necessary for his sense of logic to solve it. And again, once this is done, I would expect the scientist to make sure he can write down all the formal logic or mathematics necessary for convincing his colleagues it's all done and good. But that may come in a second stage.

    Complicated: lots of data, most of them irrelevant to the logic of the problem. Details you have to work through to get rid of. Train your brain.

    Complex: Not necessarily lots of data but ou can't simplify whatever data you have because they're all relevant to the logic of the problem.

    Yes, I made a mistaken conclusion. Next time, try to be a bit more specific. Garbage in, garbage out.

    Yes, the conceptual framework still seems wrong to me and would need to be changed. Logic just tells you there's a problem with the concepts in your framework. Which may be further evidence of our sense of logic at work.

    So explain to me entanglement.

    Sure.
    EB
     
  16. Speakpigeon Registered Senior Member

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    I provided my only answer to that but you just dismissed it.

    I said, no, the notation doesn't matter. I can't do any better.
    EB
     
  17. Speakpigeon Registered Senior Member

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    I'm not here to argue that logic is all you need to solve complex problems. But I certainly think good logic is necessary to solve any complex problem.

    My question is whether this necessary logic can be all provided by our intuitive sense of logic, or whether using formal logic becomes at some point necessary, perhaps once you get to a certain level in the complexity of the problem.

    I'm sure most problems even in science are solved by the scientist just using his sense of logic, not formal logic. My question was whether any problem ever proved too hard to do that.

    And I'm still not convinced that Bell's Theorem was such an example. It's my judgement, based on what you guys said, but I accept I may be wrong.
    EB
     
  18. iceaura Valued Senior Member

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    It is necessary in some research at all levels of complexity, for rigor in experimental design and evaluation of results and communication of the research. Everyone who uses a computer uses it.
    If it's too hard for intuitive reasoning, it's much too hard for formal logic - formal logic is more difficult to use.
    That's irrelevant. In evaluating the "answer", as well as reporting it and communicating it to others, intuition as to what is logical is insufficient. And then of course there is research, beyond the mere solving of problems.
     
  19. parmalee peripatetic artisan Valued Senior Member

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    Agreed.

    Kinda harkens back to your reference to G. Spenser Brown's Laws of Form (post #12, I think). That's one of those rare works that is mutually appreciated by those with a solid commitment to what one usually conceives as "rigor," as well as by those whom they (the rigorous sorts, that is) tend to regard as "obscurantists," or simply prone to being non-sensical.
     
  20. exchemist Valued Senior Member

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    It requires logical rigour of course, as do all observational tests. But "formal"? I don't think so. When you read a scientific paper there is plenty of description of experimental setup and the precautions against false results, but you don't get a section on logical argument.
     
  21. arfa brane call me arf Valued Senior Member

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    Yes, but he made an educated guess, or as they say, used an ansatz.

    I don't know, let's suppose he decided instead to use formal logic to describe the experimental results. Would he have found the same solution?

    What would the nature of the logical framework be?
     
  22. Speakpigeon Registered Senior Member

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    I think you, too, may be confusing coming up with possible solutions and making sure a solution is valid logically. I was't suggesting logic, let alone formal logic, could help imagine new solutions. I'm interested in the proof of potential solutions once you have them, and whether some proofs may be too complex to be dealt with just our sense of logic and require instead using formal logic.

    Here, too, this seems beside the point. I'm not interested in the whole process of science and how scientists get to agree among themselves on a new theory. As I said in the OP, it's the bit "solving scientific problems" I'm interested in.

    And then, not the "imagining" or coming up with a new concept part, only the part where you would have to use formal logic to prove the new concept.
    EB
     
  23. origin In a democracy you deserve the leaders you elect. Valued Senior Member

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    This is from the encyclopedia Britannica on Formal Logic:

    Formal logic is an a priori, and not an empirical, study. In this respect it contrasts with the natural sciences and with all other disciplines that depend on observation for their data. Its nearest analogy is to pure mathematics; indeed, many logicians and pure mathematicians would regard their respective subjects as indistinguishable, or as merely two stages of the same unified discipline.

    So I suppose you could say that Einstein had an incomplete theory that gravity is actually space being warped. He used mathematics as a proof of this to complete the theory, so that would be an application of formal logic to 'prove' the concept. Of course the real proof was the application of the theory to observation. I would say that since observation and experimentation are the foundation of science, formal logic is not really an aspect of science.
     

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